At one house, Iraq’s national flag fluttered atop a building that Iraqi soldiers had captured from militants two days before.

At another, smashed household goods and furniture were scattered on the floor.

Outside a third, hosting a meeting of Iraqi security force commanders, a captain from Iraq’s national intelligence service pointed to the far side of a murky irrigation canal.

“Here it is safe now,” he said of Al-Daira. “But over there are more terrorists. That is where we will fight them next.”

The village of Al-Daira lies about 30 miles south of Baghdad and within sight of Iraq’s main highway, in an area the American military called the Triangle of Death.

A former militant stronghold, the area is a battleground again. The Qaeda splinter group now known as the Islamic State in Iraq and Syria, or ISIS, has resumed a campaign that its predecessors started — and had appeared to lose — before the United States withdrew its troops in 2011.

The group’s tactics — a hybrid guerrilla-and-terrorist campaign of ambushes, bombings and sniper and mortar attacks, organized by fighters who blend among civilians — show that the militants are much more than a juggernaut, as lately portrayed. They are adaptive and alert to the lessons of Iraq’s insurgent past, and select different tactics for different places and situations.

While establishing themselves in Anbar, in the west, they methodically resumed the campaign south of Baghdad started by Al Qaeda in Iraq, the Sunni militant group that formed after the American invasion and swore allegiance to Osama bin Laden.